Ideal gas
The curves here represent the behavior of the gas at
different temperatures. The cooler it gets, the farther the
gas is from ideal.
In curve D, the gas becomes liquid; it begins
condensing at (b) and is entirely liquid at (a).
The point (c) is called the
critical point.
point
Below the critical temperature, the gas can liquefy if the pressure is sufficient;
above it, no amount of pressure will suffice.
• Major features of phase
diagram: triple point, critical
point and curves that represent
point,
melting points, sublimation and
boiling lines.
• At critical point: Critical
temperature: the minimum
temperature for liquefaction of
a gas using pressure, and
critical pressure: pressure
required for liquefaction. No
critical point for solid liquid
phase transition
• Rapid heating or cooling of a liquid can lead to superheating or supercooling
where liquid exists above or below its normal boiling an freezing points.
points
• Some materials made of long molecules can form liquid-crystal phase, in which
molecules move around randomly as in a liquid but still tend to be oriented
pparallel to each other.
• Boiling point: Liquids
boil when the external
pressure equals the vapor
pressure. Temperature of
boiling point increases as
pressure increases. Two
ways to get a liquid to
boil: increase temperature
or decrease pressure.
• Clausius-Clapeyron
equation gives:
At p=1 atm, the freezing and boiling of water are 0C
and 100C. The point that ice, water, and gas coexist is
called the triple point,
point defined as 273.16K
273 16K defined in
1954, International Convention.
Substance
p ~
p0 e   23 / RT
~
p  p e   23 / RT0
0
0
CO2 gas
 p 

  0,
 V Tc
(p
p
a
)(v  b)  RT
v2
RT
a
 2
vb v
RTc
2a
 p 
 3  0,
  
2
v
v
b
(
)


vc
 Tc
c
 p
2 RTc
6a
 2   
 3  0,
2

(
)

V
v
b
vc

Tc
c
2
vc  3b, RTc 
zc 
pc vc 3

RTc 8
P3(105 Pa)
Helium-4 (-point)
2.17
0.0507
Hydrogen
13.84
0.0704
Deuterium
18 63
18.63
0 171
0.171
Neon
24.57
0.432
Oxygen
54.36
0.00152
Nitrogen
63.18
0.125
Ammonia
195.40
0.0607
Sulfur dioxide
197.68
0.00167
Carbon dioxide
216.55
5.17
Water
273.16
0.0061173
 2 p 
 2   0,
 V Tc
p
V
T3(K)
8a
a
, pc 
27b
27b 2
p
pV
nRT
p
pR 
pc
Z
TR 
T
Tc
Tc((K))
Pc((bar))
He
5.2
2.29
H2
33.
12.9
N2
126
34 0
34.0
CO
133
35.0
Ar
151
48.6
O2
155
50.8
 p 
  0,

 V Tc
 2 p 
 2   0,
 V Tc
He4
Hee3
The triple
Th
t i l point
i t off a substance
bt
is
i the
th
temperature and pressure at which
three phases (liquid, gas, and solid) of
that substance may coexist in
thermodynamic equilibrium.
Friedrich Heusler (1866 – 1947) was a German
mining engineer and chemist. He discovered a
special group of intermetallics now known as
Heusler phases, which are ferromagnetic though
the constituting elements are not ferromagnetic.
Tcurie
Material
Co
Fe
FeOFe2O3*
NiOFe2O3*
CuOFe2O3*
MgOFe2O3*
MnBi
Ni
MnSb
MnOFe2O3*
Y3Fe5O12*
CrO2
MnAs
Gd
D
Dy
EuO
Curie T(K)
1388
1043
858
858
728
713
630
627
587
573
560
386
318
292
88
69
At constant T and p, the condition for phase equilibrium is ΔG=0
G  U  TS  pV  Won the system  Q  TS  Won the system  Won the system
If there is no other work, the W on the system is 0, and we have ΔG≤0.
A equilibrium,
At
ilib i
iit bbecomes reversible,
ibl andd we have
h
ΔG 0!
ΔG=0!

  
G
  
  (T0 , p0 )  
 (T  T0 )    ( p  p0 )   (T0 , p0 )   (T  T0 )   ( p  p0 )
N

T

 p,N
 p T , N
   s,   v
Example: Graphite and Diamond
μ0 (kJ/mol)
graphite
diamond
0
2.9
α (J/K/mole)
-5.74
-2.38
β (J/bar/mol)
0 541
0.541
0 342
0.342